A real-time NURBS motion interpolator for position control of a slide equilateral triangle parallel manipulator

This study presents a real-time non-uniform rational B-spline (NURBS) motion interpolator command generation for position control of a new design to achieve a six-degree-of-freedom (6dof) slide equilateral triangle parallel manipulator (SETPM). The existing method utilizes the approximate method to obtain the characteristics of curves of the velocity and acceleration for the feed-forward compensation in the joint space. However, the NURBS motion interpolator command generation is related to the geometric characteristics of curves including position, tangent, and curvature to the motion dynamics of the SETPM including position, velocity and acceleration for applied directly the feed-forward compensation in the global space. The inverse dynamics controller (IDC) is the power of control law. However, implementing the inverse dynamics control laws requires accurately knowing the system dynamic model parameters and computing the complete equations of motion in real time. To reduce the time for calculating the inverse dynamic, this study proposes a feed-forward compensation with feedback proportional derivate (PD) control to take the place of inverse dynamics control for reducing both the inverse dynamic calculation time and the tracking error. The proposed real-time NURBS motion interpolator command generation and feed-forward compensation with feedback PD control are also successfully applied to a slide equilateral triangle parallel manipulator on a PC-based system to achieve high motion precision.